Diluted quantum antiferromagnets: Spin excitations and long-range order

We have studied the static and dynamic magnetic properties of two-dimensional (2D) and quasi-two-dimensional, spin-S, quantum Heisenberg antiferromagnets diluted with spinless vacancies. Using spin-wave theory and the T-matrix approximation we have calculated the staggered magnetization M( x, T), the neutron scattering dynamical structure factor S (k,omega), the 2D magnetic correlation length xi( x, T) and, for the quasi-(2D) case, the Neel temperature T-N(x). We find that in two dimensions a hydrodynamic description of excitations in terms of spin waves breaks down at wavelengths larger than l/asimilar toe(pi/4x), x being the impurity concentration and a the lattice spacing. We find signatures of localization associated with the scale l, and interpret this scale as the localization length of magnons. The spectral function for momenta a(-1)>>k>>l(-1) consists of two distinct parts: (i) a damped quasiparticle peak at an energy c(0)kgreater than or similar toomega>>omega(0), with abnormal damping Gamma(k)similar tox c(0)k, where omega(0)similar toc(0)l(-1), c(0) is the bare spin-wave velocity; and (ii) a non-Lorentian localization peak at omegasimilar toomega(0). For kless than or similar tol(-1) these two structures merge, and the spectrum becomes incoherent. The density of states acquires a constant term, and exhibits an anomalous peak at omegasimilar toomega(0) associated with low-energy localized excitations. These anomalies lead to a substantial enhancement of the magnetic specific heat C-M at low temperatures. Although the dynamical properties are significantly modified, we show that D=2 is not the lower critical dimension for this problem. We find that at small x the average staggered magnetization at the magnetic site is M(x,0)similar or equal toS-Delta-Bx, where Delta is the zero-point spin deviation and Bsimilar or equal to21 is independent of the value of S; the Neel temperature T-N(x)similar or equal to(1-A(s)x) T-N(0), where A(s)= pi-2/pi + B/(S-Delta) is weakly S dependent. Our results are in quantitative agreement with recent Monte Carlo simulations and experimental data for S=1/2, 1, and 5/2. In our approach long-range order persists up to a high concentration of impurities x(c) which is above the classical percolation threshold x(p)approximate to0.41. This result suggests that long-range order is stable at small x, and can be lost only around xsimilar or equal tox(p) where approximations of our approach become invalid.